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2 years ago

The length of a rectangle is 4 less than 3 time the width. What is the area of the rectangle?

Mathematics

1 answer:

Talja [164]2 years ago

6 0

Use the quations 2L + 2W = Area

and L = 3W -4

Plug the second equation into the first and solve for W

2(3W-4) + 2W = A

6W - 8 + 2W= A

8W - 8 = A

8W = 8

W = 1

Then plug that into the second equation

L = 3(1) -4

L = 3 -4

L = -1

Then plug both of the answers into the first equation

2(-1) + 2(1) = A

-2 + 2 = A

0 = A

That should be the answer, but since there was no given Area, i'm not sure.

I hope this helped though!

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2 years ago

Nola purchased 2.5 pounds of cheese for $10.50. Her mother purchased 3 pounds of the same cheese for $12.60. The cost of cheese

jeka94

Answer:

cost per pound = $4.20

Step-by-step explanation:

Cheese cost per pound = ?

first for the cost per pound

cost per pound = total cost / pounds bought

cost per pound = $10.50 / 2.5 pounds

cost per pound = $4.20

to check the above answer is correct

cost per pound = total cost / pounds bought

cost per pound = $12.60 / 3 pounds

cost per pound = $4.20

Therefor, the cheese costs $4.20 per pound.

4 0

2 years ago

2x+y=x-y-3=6 What is x&y???? Please answer asap!!!!

Mariana [72]

2x + y = x - y - 3 = 6
Add 3 to everything
2x + y + 3 = x - y - 3 + 3 = 6 + 3
2x + y + 3 = x - y = 9
2x + y + 3 = 9
2x + y = 6 = x - y
Add y to everything
2x + 2y = 6 + y = x
Since x = 6 + y substitute every x with 6 + y
2(6 + y) + 2y = x
12 + 4y = x

This is as simplified as I can get and then just place 12 + 4y into every x in the original problem then solve

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3 years ago

The table below shows the cube roots of different numbers: Number (x) 27 −27 125 −125 Cube root of the number (y) 3 −3 5 −5

kolbaska11 [484]

Part A

The table does represent y as a function of x because each input (values of x) related to exactly one output. Refer to the diagram below.

Part B

We have
f(x) = 925x + 1000
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2 years ago

(1/1+sintheta)=sec^2theta-secthetatantheta pls help me verify this

Xelga [282]

Answer:

See Below.

Step-by-step explanation:

We want to verify the equation:

$\displaystyle \frac{1}{1+\sin\theta} = \sec^2\theta - \sec\theta \tan\theta$

To start, we can multiply the fraction by (1 - sin(θ)). This yields:

$\displaystyle \frac{1}{1+\sin\theta}\left(\frac{1-\sin\theta}{1-\sin\theta}\right) = \sec^2\theta - \sec\theta \tan\theta$

Simplify. The denominator uses the difference of two squares pattern:

$\displaystyle \frac{1-\sin\theta}{\underbrace{1-\sin^2\theta}_{(a+b)(a-b)=a^2-b^2}} = \sec^2\theta - \sec\theta \tan\theta$

Recall that sin²(θ) + cos²(θ) = 1. Hence, cos²(θ) = 1 - sin²(θ). Substitute:

$\displaystyle \displaystyle \frac{1-\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta \tan\theta$

Split into two separate fractions:

$\displaystyle \frac{1}{\cos^2\theta} -\frac{\sin\theta}{\cos^2\theta} = \sec^2\theta - \sec\theta\tan\theta$

Rewrite the two fractions:

$\displaystyle \left(\frac{1}{\cos\theta}\right)^2-\frac{\sin\theta}{\cos\theta}\cdot \frac{1}{\cos\theta}=\sec^2\theta - \sec\theta \tan\theta$

By definition, 1 / cos(θ) = sec(θ) and sin(θ)/cos(θ) = tan(θ). Hence:

$\displaystyle \sec^2\theta - \sec\theta\tan\theta \stackrel{\checkmark}{=} \sec^2\theta - \sec\theta\tan\theta$

Hence verified.

8 0

2 years ago